Texas's AI data centers face dual existential threats: ERCOT's independent grid operation and vulnerability to extreme weather—as demonstrated by Winter Storm Uri's 52 GW outage—coupled with escalating water scarcity threatening cooling system reliability. Existing microgrid solutions address power balance through gas turbines and energy storage but neglect cooling-water constraints as a co-equal design challenge. This study proposes a resilient microgrid architecture with water-electricity coupling for a 100 MW AI data center in West Texas, centered on a 50 MW gas turbine, 20 MWh BESS, and closed-loop cooling reservoir (310 kL) to ensure both power continuity and water security during grid outages. Nonlinear modeling reveals water as the binding constraint: an initial 120 kL design yields only 1.55 h operation under 70 MW critical load, necessitating 309 kL for 4 h survival. A three-phase rule-based IF-THEN strategy governs operation: (1) immediate grid-to-island transition with non-critical load shedding; (2) staged load reductions triggered by SOC and water thresholds; and (3) seamless grid reconnection. MATLAB/Simulink simulations replicating the 2021 Winter Storm Uri blackout scenario validate 100% critical-load (70 MW) supply over 4.2 h of islanded operation with zero external water consumption. Emergency costs amount to only 0.33% of conventional outage losses, while an optional Local Exchange Interface captures $922,500 in annual arbitrage value. The proposed framework transforms resilience from a cost center into a dual-purpose asset supporting both extreme events and daily economic optimization.